The principle \(\diamondsuit (A,B,R)\)  is a weakening of the classical \(\diamondsuit \)  principle, and has a similar relationship to \(\langle A,B,R\rangle \)  as \(\diamondsuit \)  has to \(\mathfrak {c}\) . In particular, \(\diamondsuit (A,B,R)\)  implies \(\langle A,B,R\rangle \le \aleph _1\)  (Proposition 2.5 in [1]}). The key result about \(\diamondsuit (A,B,R)\)  is as follows:
